Two photon decay and photoproduction of radial excitation of pion π0′\pi_0'

Within the framework of non-local quark model of Nambu--Jona-Lasinio type the two-photon decay of radial excited state of $\pi_0$-meson -- $\pi_0'$ -- is found to be 3.6\KeV. The radial excitation of pion is described with the use of polynomial formfactor of second order over $\vec q^2$ where $\vec q$ is the transverse momentum, which corresponds to relative motion of quark-antiquark pair within the energy range from 0 up to 1\GeV. The probabilities of production of $\pi_0'$ and $(\pi_0'+\gamma)$ states in the electron-positron colliders are estimated. The production of $\pi_0'$-meson in the interaction of photon with electron or muon is as well considered (Primakoff effect). The relevant total cross sections are 0.14 or 0.06\nb.Comment: 10 page

Processes e+e−→π0(π0′)γe^+e^-\to\pi^0({\pi^0}')\gamma in the NJL model

The processes of electron-positron annihilation into $\pi^0\gamma$ and into $\pi'(1300)\gamma$ are considered within the NJL model. Intermediate vector mesons $\rho^0$, $\omega$, $\rho'(1450)$, and $\omega'(1420)$ are taken into account. The latter two mesons are treated as the first radial excited states. They are incorporated into the NJL model by means of a polynomial form factor. Numerical predictions for the cross sections of these processes are received for the center-of-mass energies below 2 GeV. Our results for the $\pi^0\gamma$ production are in agreement with experimental data received in the energy region 600 -- 1020 MeV.Comment: 4 pages, 5 figure

Nonlocal quark model beyond mean field and QCD phase transition

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/Nc expansion scheme. The parameters of the nonlocal model are refitted to the physical values of the pion mass and the weak pion decay constant. The size of the 1/Nc correction to the quark condensate is carefully studied in the nonlocal and the usual local Nambu-Jona-Lasinio models. It is found that even the sign of the corrections can be different. This can be attributed to the mesonic cut-off of the local model. It is also found that the 1/Nc corrections lead to a lowering of the temperature of the chiral phase transition in comparison with the mean-field result. On the other hand, near the phase transition the 1/Nc expansion breaks down and a non-perturbative scheme for the inclusion of mesonic correlations is needed in order to describe the phase transition point.Comment: 4 pages, 4 figures, talk at the 3rd Joint International Hadron Structure'09 Conference, Tatranska Strba (Slovak Republic), Aug. 30-Sept. 3, 200

Radiative decays of pseudoscalar (P) and vector (V) mesons and the process e^+e^- \to \eta' \rho

Radiative decays of pseudoscalar and vector mesons are calculated in the framework of the chiral Nambu-Jona-Lasinio (NJL) model. We use the amplitude for triangle quark loops of anomalous type. In evaluating these loop integrals we use two methods. In the first one, we neglect the dependence of external momenta by reproducing the Wess-Zumino-Witten terms of effective chiral meson Lagrangian. In the second method, we take into account the momentum dependence of loop integrals omitting their imaginary part. This makes it possible to allow for quark confinement. As applied both the methods is in qualitative agreement with each other and with experimental data. The second method allows us to describe the electron-positron annihilation with production of $\eta'$ and $\rho$ mesons in the center of mass energy range from 1.6 to 3.5\GeV. The comparison with the recent experimental data is presented.Comment: 7 pages, 4 figures, 1 tabl

1/N_c- expansion of the quark condensate at finite temperature

Previously the quark and meson properties in a many quark system at finite temperature have been studied within effective QCD approaches in the Hartree approximation. In the present paper we consider the influence of the mesonic correlations on the quark self-energy and on the quark propagator within a systematic $1/N_c$- expansion. Using a general separable ansatz for the nonlocal interaction, we derive a selfconsistent equation for the $1/N_c$ correction to the quark propagator. For a separable model with cut-off formfactor, we obtain a decrease of the condensate of the order of 20\% at zero temperature. A lowering the critical temperature for the onset of the chiral restoration transition due to the inclusion of mesonic correlations is obtained what seems to be closer to the results from lattice calculations.Comment: 19 pages, REVTeX, 5 figure

Scalar Mesons in a Chiral Quark Model with Glueball

Ground-state scalar isoscalar mesons and a scalar glueball are described in a U(3)xU(3) chiral quark model of the Nambu--Jona-Lasinio (NJL) type with 't Hooft interaction. The latter interaction produces singlet-octet mixing in the scalar and pseudoscalar sectors. The glueball is introduced into the effective meson Lagrangian as a dilaton on the base of scale invariance. The mixing of the glueball with scalar isoscalar quarkonia and amplitudes of their decays into two pseudoscalar mesons are shown to be proportional to current quark masses, vanishing in the chiral limit. Mass spectra of the scalar mesons and the glueball and their main modes of strong decay are described.Comment: 10 pages, LaTeX text, requires svjour.cls and svepj.cl

Light Quark Masses in Multi-Quark Interactions

We suggest and discuss in detail a multi-quark three flavor Lagrangian of the Nambu -- Jona-Lasinio type, which includes a set of effective interactions proportional to the current quark masses. It is shown that within the dynamical chiral symmetry breaking regime, the masses of the pseudo Goldstone bosons and their chiral partners, members of the low lying scalar nonet, are in perfect agreement with current phenomenological expectations. The role of the new interactions is analyzed.Comment: 8 pages, published versio

Density Effect on Hadronization of a Quark Plasma

The hadronization cross section in a quark plasma at finite temperature and density is calculated in the framework of Nambu--Jona-lasinio model with explicit chiral symmetry breaking. In apposition to the familiar temperature effect, the quark plasma at high density begins to hadronize suddenly. It leads to a sudden and strong increase of final state pions in relativistic heavy ion collisions which may be considered as a clear signature of chiral symmetry restoration.Comment: Latex2e, 11 pages, 7 Postscript figures, submitted to Phys. Rev.

Abnormal number of Nambu-Goldstone bosons in the color-asymmetric 2SC phase of an NJL-type model

We consider an extended Nambu--Jona-Lasinio model including both (q \bar q)- and (qq)-interactions with two light-quark flavors in the presence of a single (quark density) chemical potential. In the color superconducting phase of the quark matter the color SU(3) symmetry is spontaneously broken down to SU(2). If the usual counting of Goldstone bosons would apply, five Nambu-Goldstone (NG) bosons corresponding to the five broken color generators should appear in the mass spectrum. Unlike that expectation, we find only three gapless diquark excitations of quark matter. One of them is an SU(2)-singlet, the remaining two form an SU(2)-(anti)doublet and have a quadratic dispersion law in the small momentum limit. These results are in agreement with the Nielsen-Chadha theorem, according to which NG-bosons in Lorentz-noninvariant systems, having a quadratic dispersion law, must be counted differently. The origin of the abnormal number of NG-bosons is shown to be related to a nonvanishing expectation value of the color charge operator Q_8 reflecting the lack of color neutrality of the ground state. Finally, by requiring color neutrality, two massive diquarks are argued to become massless, resulting in a normal number of five NG-bosons with usual linear dispersion laws.Comment: 13 pages, 4 figures, revtex

Virtual Compton Scattering off the Pseudoscalar Meson Octet

We present a calculation of the virtual Compton scattering amplitude for the pseudoscalar meson octet in the framework of chiral perturbation theory at ${\cal O}(p^4)$. We calculate the electromagnetic generalized polarizabilities and compare the results in the real Compton scattering limit to available experimental values. Finally, we give predictions for the differential cross section of electron-meson bremsstrahlung.Comment: 9 pages, Latex, uses cjp3.sty (included), 4 eps figures, to be published in the proceedings of the 13th Indian-Summer School "Understanding the Structure of Hadrons," August 28 - September 1, 2000, Prague, Czech Republi